Grade 7 · Unit 1 · Lesson 3 · part 2 of 5

Two names for one number

In Lesson 2 you divided every row of a table and looked for the same number.

Two names for one number

In Lesson 2 you divided every row of a table and looked for the same number. That number has two names, and both matter.

Unit rateHow much for one. The lemonade number, 0.75, is the cost of one cup.

Constant of proportionalityThe same number, with its formal name. Constant means it never changes, like a constant noise that keeps going and going. So the constant of proportionality is the number the relationship always multiplies by.

A proportional relationship always multiplies by the same number, the unit rate.

Same number, two names. When a teacher says constant of proportionality, hear the unit rate, the number that never changes. The unpacking of the NC standards calls it the most important thing to find in a proportional relationship, and this whole year keeps coming back to it.

You can find it in four places. This lesson does the first two. Lessons 4 and 5 do the graph and the equation.

From a table

Divide any output by its input. Lemonade: 2.25 ÷ 3 = 0.75.

From words

A landscaper charges $140 for 4 hours. 140 ÷ 4 = 35, so $35 an hour.

From a graph

Go over to 1 and read up to the line. Lesson 4.

From an equation

In y = rx, it is r. Lesson 5.

Where to go next

Next: Which pairs fit?The landscaper's fee is proportional: $35 for every hour, always multiplying by 35. All the partsThe Unit Rate